PROBLEMS
233
PROBLEMS
9.1 Determine the number of total flops as a (unction of the number of equations ii for the tridi agonal algorithm Fig. 9.2 1_ se the eraph teal net h d ti solve = 24 3v

b Substitute our results cheek our ans 9.7 Gis en the equatio
Thermocline?
EE 231_B1 Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov Damir Iraliyev, 1246540 Assignment 9 14.2 Using the same approach as was employed to derive Eqs.(13.15) and (13.16), derive the least sq
PROBLEMS
109
because these errors are minimal on the time and space scales associated with the bungee jumper problem. However, suppose that air resistance is not proportional to the square of the fall velocity, as in Eq. (1.7), but is related to velocity
EE 231_B1 Numerical Analysis for Electrical and Computer Engineering Course Instructor: Dr. Sergiy Vorobyov
Solutions to Assignment 9
14.2 The sum of the squares of the residuals for this case can be written as
Sr =
(y
n i =1
i
a1 x i a 2 xi2
)
2
The pa
r
422
NUMERICAL INTEGRATION FORMULAS
continued
Underestimates
10
C 0
30
.1,
ft
RGURE 17 20 CrapLca Hec .I r\ so. arca 1 ic pa tLc:a cas B a 5 ,r ra fl( to aol I
rirar.:JI
u a

.fl a
(O
h
1aco
J
i
pe
ad
a
determine an improved integral estimate. For exam
EE 231_B1 Damir Iraliyev 1246540 Homework#5:
Question7.4 Given a function fx=1.5x6+2x4+12x a) Plot the function b) Use analytical Methods to prove that the function is concave for all values of x c) Differentiate the function and then use rootlocation m
Ee231_B1_Vorobyov Damir_Iraliyev_1246540 Assignment 6 9.5 Given equations: 1 0.5x1x2=9.5 2 1.02x12x2=18.8 (a) Solve graphically. (b) Compute the determinant. (c) On the basis of (a) and (b), what would you expect regarding the systems conditions? (d)
EE 231_B1 Damir Iraliyev 1246540 Homework#7:
Question11.3 The following system of equation is designed to determine concentrations (the cs in g/ m3) in a series of coupled reactors as function of the amount of mass input to each reactor (the righthand si
EE 231_B1 Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov Damir Iraliyev, 1246540 Assignment 9 14.2 Using the same approach as was employed to derive Eqs.(13.15) and (13.16), derive the least squares fit of
_
_
_
332
GENERAL LINEAR LEASTSQUARES AND NONLINE AR REGRESSION
PROBLEMS
14.1 Fit a parabola to the data from Table 13.1 Determine the r for the fit and com 2 ment on the efficacy of the result. 14.2 Using the same approach as was employed to derive Eqs.
EE 231_B1 Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov
Solutions to Assignment 8
13.2 The data can be sorted and then grouped. We assume that if a number falls on the border between bins, it is placed in
312
LINEAR REGRESSION
continued
bestfit line folloss a Gaussian distribution, and that the standa rd deviation is the same at e er) \ alue of the dependent variable. These assumptions are rarely true after transforming data. As a consequence of the last
2010 EE 231_2009 winter Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov
Solutions to Assignment 1
1.7 (a) The first two steps are
The process can be continued to yield
t 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
_
fl
PROBLEMS
39
continued
increases. Based on this result, you might conclude that your model needs to be improved. At the least, it might motivate you to conduct further experim ents with a larger number of jumpers to confirm your preliminary finding. I
EE 231_B1 Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov
Solutions to Assignment 3
4.3
function ep = macheps % determines the machine epsilon e = 1; while (1) if e+1<=1, break, end e = e/2; end ep = 2*e; >
/4s3
I
vQw
4,
=
136
5.6 (a) Determine
ROOTS: BRACKETING METHODS
case, the width and the crosssectional area can be related to depth v by B=3+y and A
3y +
the roots of f(x) = 14 20x + 23 19x 3x graphically. In addition, determine the first root of the fun
PROBLEMS
45$
An Mfile can be developed to hold the potential energy function:
183
continued
Sohton,
function p=PE (x, ka, kb, La, Lb, 91, 92)
W=F1*X(1)+92*x(2) p=PEa+PEbW;
The solution can be obtained with the fminsearch function:
>
ka=9 ; kb=2 La1O Lb=
EE 231_Bi Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov
7.4 (a) The function can be plotted
C
/
50
100 2
1.5
1
0.5
C
0.5
1
1.5
(b) The function can be differentiated twice to give 42 fz45x +24x
The se
EE 231_B1 Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov
Solutions to Assignment 6
9.5 (a) The equations can be expressed in a format that is compatible with graphing x versus x :
2 1
The resulting plot ind
_
_
PROBLEMS
261
Sote that the
same
computation would he made in MATLAB as
Implementing both remedies sould reduce the concentration hr 10.345 rng/m. The result ould bring the kids room concentration to 12.345 10.345 = 2 rngIrn. This makes sense, because
EE 231_B1 Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov
Solutions to Assignment 7
11.3 The following solution is generated with MATLAB. (a)
> A = [15 3 1;3 18 6;4 1 12]; > format long > AI = inv(A) A
EE 231_2010 winter Numerical Analysis for Electrical and Computer Engineers Course Instructor: Dr. Sergiy Vorobyov
Assignment 1
1.7 The amount of a uniformly distributed radioactive contaminant contained in a close reactor is measure by its concentration